Filter structures using bimodal, bisymmetric networks

ABSTRACT

A variety of filter structures are synthesized by means of a cascade of bimodal networks. By including mode converters between adjacent pairs of networks, successive networks can be made to respond to one or the other of said modes. A transmission line filter and a coupler (channel dropping) filter are described.

United States Patent Inventor Harold Seidel Warren Township, Somerset County, NJ. Appl. No. 776,398 Filed Nov. 18, 1968 Patented Sept. 14, 1971 Assignee Bell Telephone Laboratories, Inc.

Murray Hill, NJ.

FILTER STRUCTURES USING BIMODAL,

BISYMMETRIC NETWORKS 8 Claims, 21 Drawing Figs.

[1.8. CI 333/73 R, 333/21 R, 333/11, 333/31 Int. Cl. H0311 7/10 Field otSearch 333/73,73 C, 11, 31, 21, 10

I9 F I 3 I CONVERTER-l5 SIGNAL SOURCE 1 INPUT COUPLING NETWORK-ll TERll/llNATlON-ZB Mob? CONVERTER-l6 BIMODAL NETWORK- l2 Primary Examiner-Herman Karl Saalbach Assistant Examiner-Saxfield Chatrnon, Jr. Attorneys-R. J. Guenther and Arthur J. Torsiglier ABSTRACT: A variety of filter structures are synthesized by means of a cascade of bimodal networks By including mode converters between adjacent pairs of networks, successive networks can be made to respond to one or the other of said modes. A transmission line filter and a coupler (channel dropping) filter are described.

M065 2o CONVERTER-17 3 3 NETWORK (BIMODAL BIMODAL I 4 4 NETWORK-13 NETWORK-l4 \FILTER- Q LOAD-22 FILTER STRUCTURES USING BIMODAL. BISYMMETRIC NETWORKS This invention relates to filter circuits employing multimode network sections.

BACKGROUND OF THE INVENTION It is customary to think of circuits in terms of two-ports, such as inductors, capacitors and resistors. These basic components, in addition to being the traditional circuit components, can be made very inexpensively and are sufficiently small to permit their use in very large numbers. Recently, however, the quadrature hybrid coupler has been developed to such a state where it too can be made to be very inexpensive and very small, thus providing the circuit designer with an additional basic circuit component having a variety of interesting and useful properties.

To construct a filter using two-ports, however, requires that the two-port components be arranged in distinctly different ways in order to form the necessary combinations of series and shunt circuits needed to synthesize characteristic. desired filter characteristic.

Four-ports, on the other hand, are bimodal and, as such, are characterized by two different normal modes and two different modal responses. As a consequence, the same circuit component can be used to produce distinctly different network effects within a filter circuit.

One of the better known of the four-ports is the quadrature hybrid coupler. As is known, a quadrature hybrid coupler maintains an impedance match over a relatively broad frequency range. As such, it is particularly useful in systems requiring low loss, impedance-matched conditions over a wide frequency range. This, typically, is the case, for example, in systems using tunnel diodes, since they are known to exhibit a negative resistance over a range of frequencies which extend down to direct current. This potential for instability, accordingly, requires that circuits used with such active elements, such as filters, for example, be impedance-matched both outside, as well as within the frequency band of interest.

It is, accordingly, the broad object of the present invention to synthesize filters using bimodal network sections such as quadrature hybrid couplers.

SUMMARY OF THE INVENTION A filter in accordance with the present invention comprises a plurality of cascaded four-ports, all of which are characterized by the same pair of normal propagating modes. Adjacent pairs of four-ports are coupled together by means of a mode converter which converts all the energy from one to the other of said modes.

In one of the embodiments to be described in greater detail hereinbelow, a transmission line filter is synthesized using sections of twin-conductor coaxial cable coupled together by a phase shifter which introduces a 180 relative phase shift between signal components propagating along the two inner conductors.

In a second embodiment of the invention, a coupler filter is synthesized by cascading quadrature hybrid couplers.

It is a feature of the present invention that, though distinctly independent of each other, the different modal responses of a four-port are made simultaneously available. Thus, the same four-port can be used throughout the filter to simulate either a series or a shunt network component These and other objects and advantages, the nature of the present invention, and its various features, will appear more fully upon consideration of the various illustrative embodiments now to be described in detail in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 shows, in block diagram, a filter in accordance with the present invention;

FIG. 2 shows a first specific embodiment of the invention employing twin-conductor coaxial cable as'a bimodal network;

of ports, and the symmetric mode equivalent circuits of the coupler with respect to the selectedports;

FIG. 9 shows the symmetric mode equivalent circuit of each network section of FIG. 4;

FIGS. 10A, 1013, 11A and 11B show a quadrature coupler excited in the antisymmetric mode with respect to selected pairs of ports, and theantisymmetric mode equivalent circuits of the coupler with respectto the selected ports;

FIG. 12 shows the antisymmetric mode equivalentcircuit of each network section of FIG. 4;

FIG. 13 shows the equivalent circuit of the filter of FIG. 4 excited in a symmetric mode;

FIG. 14 shows the equivalent circuit of the filter of FIG. 4 excited in the antisymmetric mode;

FIG. 15 shows a signal source coupled to one port of the filter of FIG. 4; a nd 7 FIGS. 16 and 17 show the symmetric mode and the antisymmetric mode equivalents of the manner of excitation shown in FIG. 15.

DETAILED DESCRIPTION Referring to the drawings, FIG. 1 shows a filter 10, in accordance with the present invention, comprising a plurality of cascaded bimodal network sections 11, 12, 13 and 14 coupled together by means of mode converters 1,5, 16 and 17. A signal source 18 is coupled to ports I and 2 of filter 10 through port 1 of a four-port input coupling network 19. Port 2 of input network 19 is resistively terminated.

At its output end, ports 3 and 4 of filter 10 are coupled through a four-port output coupling network 20 to a load 21 connected to port 1 of coupling network 20. Terminal 2 of network 20 is resistively terminated.

While four networks and three mode converters are shown in FIG. 1, it is understood that, in general, the number of network sections used in any specific instance will depend upon the particular application at hand and, as such, can vary from a minimum of two sections, coupled together by means of a single mode converter, to an unspecified maximum number of sections.

All of the bimodal networks 11 through 14 are characterized by the same pair of normal propagating modes, where the term normal mode refers to a specified configuration of excitation that remains uniform throughout the network. As such, they can either be similar networks in which the network configurations are the same but in which thenetwork parameters are different, or they can be identical networks. In either instance, each network sectionresponds differently to the two different modes of excitation. Thus, in operation, a signal derived from signal source 18, and coupled to, the input end of filter l0, propagates through networkll in one modal con-' figuration and elicits a corresponding responsefrom the network. The signal then traversesmode converter 15 wherein the modal configuration is changedtoa-second mode of excitation. The effect is to elicit a correspondingly different,

response from network 12. The process of converting back and forth between modes, as a means of producing a different response from adjacent network sections, continues until the last network section 14 is reached. The net output signal derived from this filter, and coupled to output circuit 20, is a function of the cascade of the responses elicited from each of the network sections, and as such can be shaped by the proper selection of circuit parameters and modes.

A simple embodiment of such a filter is illustrated in FIG. 2. As shown, each network 11, 12, 13 and 14 is a section of twinconductor coaxial transmission line comprising a pair of inner conductors 30 and 31, symmetrically located with respect to the transmission line axis zz, surrounded by an outer conductor 32. Mode converters 15, 16 and 17 comprise phase-inverting transformers 24, 25 and 26, respectively, connected between one of the inner conductors 30 and outer conductor 32 in a manner to couple adjacent segments of conductor 30.

The filter is energized by means of signal source 18 connected to port 1 of input coupling network 19. Port 2 of network 19 is resistively terminated, and ports 3 and 4 are connected to conductors 31 and 30, respectively. Input coupling network 19 comprises a hybrid transformer such that when signal source 18 is connected to port 1, as in FIG. 2, conductors 30 and 31 are energized in phase, or in the symmetric mode. If, on the other hand, signal source 18 were connected to port 2, conductors 30 and 31 would be energized 180 out of phase, or in the antisymmetric mode. At the output end of the filter, output coupling network 20 comprises a second hybrid transformerwhose output ports 1 and 2 are connected to loads 21 and 22. When ports 3 and 4 are energized in phase, all the signal is coupled to load 21. When ports 3 and 4 are energized out of phase, all the signal energy is coupled to port 2 and load 22.

With signal source 18 connected to port 1 of network 19, as shown in FIG. 2, conductors 30 and 31 are energized in phase. As a result, both inner conductors are at the same potential and the section of transmission line comprising bimodal network 11 appears, insofar as the signal is concerned, as a length of coaxial transmission line of characteristic impedance 2,. Upon reaching the end of section 11, however, the signal in conductor 30 undergoes a 180 relative phase shift in transformer with respect to the signal in conductor 31. As a consequence, the signals in the two inner conductors are now equal in amplitude but 180 out of phase, or in the antisymmetric mode. Section 12, as a result, appears to the signals as a two-wire section of transmission line of characteristic impedance 2,, where 2 is less than Z,.

At the next mode converter 16, the signals experience a second 180 relative phase shift, restoring the symmetric mode of excitation to conductors 30 and 31. Accordingly, section 13 appears as a section of coaxial transmission line of characteristic impedance Z,. Similarly, section 14, energized in the antisymmetric mode, appears as a section of line of lower impedance 2 FIG. 3 is a symbolic representation of the filter of FIG. 2 showing alternate sections of transmission line of impedance 2,, followed by a section of lower impedance 2,. It will be noted that by exploiting the different modal responses of a twin-conductor coaxial transmission line, distinctly different electrical characteristics are realized without changing the physical structure of the line. More generally, the introduction of periodic modal transitions along a bimodal structure has the effect of cascading the network characteristics of the two modes.

FIG. 4 shows an embodiment of a coupler filter 40, in accordance with the present invention, comprising a cascade of quadrature hybrid couplers 41 through 46 where the term quadrature hybrid coupler" is used in its accepted sense to describe a power-dividing network having four ports in which the ports are arranged in pairs with the ports comprising each pair being conjugate to each other and in coupling relationship with the ports of the other of said pairs. In addition, the divided signal components are 90 out of time phase, hence the designation quadrature? coupler. Examples of such hybrids are the Riblet coupler (H. J. Riblet "The Short-Slot Hybrid Junction," Proceedings of the Institute of Radio Engineers, Feb. 1952, pages 180-484), the multiple directional coupler (S. E. Miller, Coupled Wave Theory and Waveguide Applications," Bell System Technical Journal, May 1954 pages 661-719), the semiopticai directional coupler (E. A. J. Marcatili, "A Circular Electric Hybrid Junction and Some Channel-Dropping Filters," Bell System Technical Journal, Jan. 1961, pages 185-196), the strip transmission line directional coupler (T. K. Shimizu "Strip-line 3 db. Directional Coupler, 1957 Institute of Radio Engineers, Wescon Convention Record, Vol. 1, Part 1, pages 4-15), and the lumped-element quadrature hybrid couplers disclosed in the copending application Ser. No. 709,091., filed Feb. 28, 1968 by H. R. Beurrier and assigned to applicants assignee.

As will now be shown, the principles of the present invention can be applied to quadrature hybrid couplers to synthesize a variety of coupler filter structures. For purposes of explanation, particular attention will be directed to the lumpedelement type of coupler since it is the simplest to describe. However, it is to be understood that the results and conclusions to be drawn are equally applicable to all of the various types of quadrature couplers.

As described in the above-identified application by H. R. Beurrier, a lumped-element coupler comprises a pair of conductively insulated conductors whose electrical length is a small fraction of a wavelength at the operating frequencies. Lengths of the order of one-eight of a wavelength and less are typical. The conductors can either be twisted about each other as a means of maintaining a constant orientation with respect to each other, or they can be mounted on opposite sides of a dielectric material.

Because of its short electrical length, the equivalent circuit of such a coupler can be represented by lumped-impedance elements as shown in FIG. 5 wherein the two conductors as represented by two, tightly coupled inductors 50 and 51. The conductor-to-corrductor capacitance is represented by the two capacitors 52 and 53. The four coupler ports are identified by the numerals l, 2, 3 and 4 of which ports 1 and 4 comprise one pair of conjugate ports and ports 2 and 3 are the other pair.

As explained by Beurrier, if the self-inductance of each conductor is L, and the total conductor-to-conductor capacitance is C, the characteristic impedance Z, of the coupler is given by The signal distribution, as a function of frequency, is given by curves 60 and 61 in FIG. 6, which show the amplitudes of the transmitted signal component t and of the quadrature reflected signal component k, where Basically, the transmitted component is a maximum at zero frequency and decreases as the frequency increases. The reflected component, on the other hand, is a minimum at zero frequency, and increases as the frequency increases. The two components are equal at the crossover frequency to As can be seen from the equivalent circuit of FIG. 5, a quadrature hybrid coupler is bisymmetrical with respect to two, mutually perpendicular axes z-z and y-y, each of which bisects the coupler into two, identical two ports. The latter are referred to as bisected prototypes" and can be conveniently used to study the coupler since each has within it all the properties of the original four-port. The coupler is also bidual, as will be shown hereinbelow by separately exciting the coupler in the symmetric and antisymmetric modes.

Referring again to FIG. 4, the couplers comprising filter 40 are arranged in pairs 41-42, 43-44 and 45-46, where each pair corresponds, respectively, to one of the bimodal network sections 11, 12 and 13 of FIG. I. With respect to each pair, the second coupler is rotated with respect to the first coupler such that a pair of ports 3 and 4, symmetrically situated with respect to one of the axes of symmetry, is coupled to a pair of ports 1 and 3 that are symmetrically located with respect to the other axis of symmetry.

Adjacent network sections are coupled together by means of relative phase shifters 47 and 48 located in one of the interconnecting wavepaths. These phase shifters correspond to mode converters and 16 ofFIG. 1.

Port 1 of hybrid 41 is the filter input port to which a signal source 49 is connected. Output signals are taken from port 2 of the first hybrid 41 and from port 2 of the last hybrid 46. Port 4 of hybrid 46 is resistively terminated.

While only three bimodal network sections are shown, it is understood that, as indicated hereinabove, additional sections can be added as required.

The operation and characteristics of filter 40 will now be examined by first examining the modal characteristics of a quadrature hybrid coupler with respect to its two symmetry axes.

SYMMETRIC MODE REPRESENTATION The modal characteristics of the coupler are determined by exciting the coupler in its normal modes and observing the responses thereto produced by the coupler. These responses, while they take into account all internal interactions, are represented only with respect to their externally observable manifestations. Thus, for example, the modal response representations do not concern themselves with mutual inductive effects since, for any specific mode, this internal interaction is uniquely defined and is included in the externally observed response.

The first modal response to be examined is the symmetric mode with respect to ports 1 and 2 (and, because of the symmetry of the coupler, with respect to ports-3 and 4). This is determined by energizing ports 1 and 2 by means of two, equal amplitude, in phase signal sources 70 and 71, as illustrated in FIG. 7A. Ports 3 and 4 are match-terminated. Since inductors 50 and 51 are always at the same potential when ports 1 and 2 are energized in the symmetric mode, there is no capacitive current flow and each of the signals sees a symmetric mode impedance L, which is inductive, and which, because the mutual inductance between the two conductors is close to unity, is approximately equal to 21... Thus, the equivalent circuit of the coupler in the symmetric mode domain, with respect to ports 1 and 2 (and ports 3 and 4) comprises a pair of series inductors of magnitude L,=2L, as illustrated in FIG. 73. It should again be noted that in this modal representation, there is no mutual coupling between inductors L,.

The symmetric mode equivalent circuit with respect to ports 1 and 3 and, because of the symmetry of the coupler, between ports 2 and 4, is determined by energizing ports 1 and 3 by means of two, equal amplitude, in phase signal sources 72 and 73, as illustrated in FIG. 8A, Since opposite ends of inductors 50 and 51 are always at the same potential when ports 1 and 3 are energized in the symmetric mode, there is no inductive current flow. The only current flow is through capacitors 52 and 53. Thus, the equivalent circuit of the coupler in the symmetric mode domain with respect to ports 1 and 3 (and ports 2 and 4) comprises a pair of series capacitors of magnitude C,=C2, as illustrated in FIG. 8B.

The symmetric mode equivalent circuit for each of the bimodal network sections 11, 12 and 13 of filter 40 is obtained by cascading the equivalent circuits of FIGS. 7B and 88 as in FIG. 9. As can be seen, the result is a simple series L-C circuit whose resonant frequency w, is given by 41.,0' (4) Substituting 2L for L, and C/2 2 for C,, gives frequencies and the resonant frequency of the equivalent circuit can all be different.

ANTISYMMETRIC MODE REPRESENTATION The antisymmetric mode equivalent circuit, with respect to ports 1 and 2, is derived by connecting ports 1 and 2 to opposite terminals of a common signal source 80, as shown in FIG. 10A. Ports 3 and 4 are resistively terminated. Excited in this manner, conductors 50 and 51 are energized l out of phase. As a consequence, the currents in the two conductors flow in opposite directions, producing no net component of inductive current. The only net current flow is capacitive, due to the interconductor capacitance represented by capacitors 52 and 53. Accordingly, with respect to ports 1 and 2 (and 3 and 4), the antisymmetric equivalent circuit, shown in FIG. 108, comprises a shunt capacitance C equal to the couplers conductor-to-conductor capacitance C, connected between terminals 1 and 2 (and 3 and 4).

The antisymmetric mode equivalent circuit with respect to ports 1 and 3 (and 2 and 4) is derived'by connecting a signal source 81 between ports 1 and 3, as illustrated in FIG. 11A. Because of the tight coupling between inductors 50 and 51 (M= l the two inductors are essentially at the same potential and there is no net capacitive current flow. The equivalent circuit of the coupler in the antisymmetric mode with respect to ports 1 and 3 (and 2 and 4) is, therefore, as shown in FIG. 11B, a shunt inductance L equal to the self-inductance L of a single inductor.

FIG. 12, comprising a cascade of the equivalent circuits of FIGS. 10B and 118, gives the antisymmetric mode equivalent circuit of each of the bimodal network sections 1 l, 12 and 13 of filter 40. Since C,,,=C and L,,,=L, the circuit is a simple shunt L-C circuit whose resonant frequency m is equal to the crossover frequency of the two couplers comprising each section.

It will be further noted that since the symmetric mode equivalent circuits (FIGS. 78 and 8B) are the network duals of the antisymmetric mode equivalent circuits (FIGS. 10B and 118) the lumped element quadrature coupler is seen to be bidual. This, in general is the characteristic of all quadrature hybrid couplers. The actual circuits, however, tend to be more complex for the distributed, or transmission line type couplers.

It is evident that merely to cascade network sections would not produce the desired filter configuration since such a cascade would comprise a cascade of series L-C circuit when energized in the symmetric mode, and a cascade of parallel L- C circuits when energized in the antisymmetric mode. What is required, therefore, is a means for converting between modes such that whatever mode of excitation is applied to the first section is converted to the other mode at the second and subsequent even-numbered network sections in the cascade, and is converted back to the incident mode of excitation at all subsequent odd-numbered network sections. This mode conversion function is provided by the relative phase shifters 47 and 48 located between adjacent network sections 1 1-12 and 12-13, respectively. Thus, for example, phase shifter 47 serves to convert symmetric mode excitation applied to the input ports 1-2 of hybrid 41 to the antisymmetric mode of excitation at terminals 1-2 of hybrid 43. Thus, the first bimodal network 11 appears as a series L-C circuit in response to the symmetric mode of excitation applied to it, whereas the second bimodal network 12 appears as a shunt L-C circuit in response to the antisymmetric mode of excitation applied to it. Similarly, the third network is excited in the symmetric mode and appears as a series L-C network.

The equivalent circuit of filter 40, excited in the symmetric mode, is shown in FIG. 13. It comprises the series circuit of network 11, the parallel circuit of network 12 and the series circuit of network 13.

If, on the other hand, ports 1 and 2 of hybrid 41 are excited in the antisymmetric mode, the first and third networks 11 and l3 respond in the antisymmetric mode, shunt L-C equivalent, whereas network 12 responds in the symmetric mode, series L-C equivalent. The equivalent filter circuit for the antisymmetric mode of excitation is illustrated in FIG. 14. The latter, it will be noted, is the network dual of the circuit shown in FIG. 13.

In practice, however, filter 40 is typically not excited exclusively in either the symmetric or the antisymmetric mode, but rather in both modes simultaneously. That this is so can be seen by referring to FIG. 15 which shows a signal source 49 connected to port 1 of the first hybrid 41. With respect to ground, therefore, the signal applied to port 1 is +E whereas the signal applied to port 2 is zero. This manner of excitation can be considered, however, to comprise two components. The first is a symmetric mode of +E/2 applied to both ports, and the second, an antisymmetric mode of +E/2 applied to port 1 and E/2 applied to port 2. The sum of these two at port 1 is +E, while the sum at port 2 is zero. We can, therefore, analyze the response of the filter to each of the two modes separately, and then sum these responses to obtain the total response.

This is now done with reference to FIGS. 16 and 17 which show the overall signal distribution at the four ports of the filter in response to the symmetric and antisymmetric modes of excitation.

Referring to FIG. 16, a symmetric mode signal of amplitude E/2, applied to ports 1 and 2 of the first hybrid coupler 41 produces a transmitted signal component 13/21, at each of ports 2 and 4 of coupler 46, and produces a reflected signal component (E/2)k, at each of ports 1 and 2 of hybrid 41, where t, is the symmetric mode coefficient of transmission for the filter, and k, is the symmetric mode coefficient of reflection for the filter.

FIG. 16 shows the response to the antisymmetric mode signal of +E/2 applied to port 1 of coupler 41 and E/2 applied to port 2 of coupler 41. Signal E/2 produces a transmitted signal in port 2 of coupler 46 of (E/2)r,, and a reflected signal component E/2)k,,, in port 1 of coupler 41. Similarly, signal E/2 produces a transmitted signal component E/2)! in port 4 of coupler 46 and a reflected signal component -(E/2 )as in port 2 of coupler 41, where t is the antisymmetric mode coefficient of transmission for the filter, and k,,, is the antisymmetric mode (E/2 of reflection for the filter.

Since the symmetric and antisymmetric mode equivalent circuits are network duals of each other, they have the same coefficients of transmission whereas their coefficients of reflection are the negatives of each other. That is s us By superposition, the net signal at each of the ports can be obtained by summing the normal mode responses at each of the ports when the filter is energized at port 1 of coupler 41 in the manner indicated in FIG. 15.

At port 1 of coupler 41, the reflected signal E,, is

Thus, the filter is reflectionless.

The reflected signal E at port 2 of coupler 41 is r2=( i (E/2)k,,,=Ek, (9 The transmitted signal E at port 2 of coupler 46 e=(E/2) /2)r,,,=Er, 10)

The transmitted signal E at port of coupler 46 Thus, the signal applied to pen 1 of coupler 4 l divides between port 2 of coupler 41 and port 2 of coupler 46 in proportion to k, and t,. Since both I, and k, vary with frequency, a roadband signal applled to the filter is divided such that one It has been shown that while a bimodal network can be characterized by two manually independent modal responses, both can, nevertheless, be made simultaneously available notwithstanding their independence. It has also been shown that the modal responses can be used to synthesize a variety of filter structures. While only two specific filter circuits have been described in detail, it is understood that the abovedescribed arrangements are merely illustrative of but a small number of the many possible specific embodiments which can represent applications of the principles of the invention. For example, at the higher frequencies a filter similar to that shown in FIG. 2 can be synthesized using a conductively bounded transmission line instead of a twin-conductor coaxial cable since it is known that the various transmission modes have different field distributions and, hence, a distinctly different modal response is produced by discontinuities at a particular location within the waveguide. Similarly, the different response of gyromagnetic materials to oppositely rotating circularly polarized waves can be exploited in a manner consistent with the principles disclosed hereinabove by a judicious array of longitudinally spaced half waveplates. Thus numerous and varied other arrangements can readily be devised in accordance with these principles by those skilled in the art without departing from the spirit and scope of the invention.

Iclaim:

l. A filter comprising:

a cascade of bisymmetrical, bimodal networks all of which are characterized by the same two normal modes;

and means, connecting adjacent pairs of said networks, for

converting all of the wave energy from one of said normal modes in one network to the other of said normal modes in the next adjacent network.

2. The filter according to claim 1 wherein each network comprises a section of cable having two inner conductors surrounded by an outer conductor;

and wherein said mode converter comprises means for introducing relative phase shift between signal components propagating along said two inner conductors.

3. The filter according to claim 1 including means for externally energizing said filter in at least one of said modes.

4. The filter according to claim 1 including a signal source for simultaneously energizing an external port of said filter in both of said modes.

5. The filter according to claim 1 wherein each of said networks is a four-port.

6. The filter according to claim 1 where each of said networks comprises a pair of coupled four-ports, each of which has two axes of symmetry;

and wherein two of the ports, symmetrically disposed with respect to one of the axis of one of said four-ports, are connected respectively to two of the ports, symmetrically disposed with respect to the other of said axes, of the other of said four-ports.

7 The filter according to claim 6 wherein each of said fourports is a quadrature hybrid coupler.

8. The filter according to claim I wherein each of said bimodal networks is bidual. 

1. A filter comprising: a cascade of bisymmetrical, bimodal networks all of which are characterized by the same two normal modes; and means, connecting adjacent pairs of said networks, for converting all of the wave energy from one of said normal modes in one network to the other of said normal modes in the next adjacent network.
 2. The filter according to claim 1 wherein each network comprises a section of cable having two inner conductors surrounded by an outer conductor; and wherein said mode converter comprises means for introducing 180* relative phase shift between signal components propagating along said two inner conductors.
 3. The filter according to claim 1 including means for externally energizing said filter in at least one of said modes.
 4. The filter according to claim 1 including a signal source for simultaneously energizing an external port of said filter in both of said modes.
 5. The filter according to claim 1 wherein each of said networks is a four-port.
 6. The filter according to claim 1 where each of said networks comprises a pair of coupled four-ports, each of which has two axes of symmetry; and wherein two of the ports, symmetrically disposed with respect to one of the axis of one of said four-ports, are connected respectively to two of the ports, symmetrically disposed with respect to the other of said axes, of the other of said four-ports.
 7. The filter according to claim 6 wherein each of said four-ports is a quadrature hybrid coupler.
 8. The filter according to claim 1 wherein each of said bimodal networks is bidual. 